Do I even need a dedicated stereo preamp?

Agree with kennymacc. Suggest you connect with a friend and see if you can borrow a half-decent pre-amp and just try it for an evening or longer.

I was excited to directly connect my Pegasus Musician DAC to my Shanling tube power monoblocs with gain control... fully anticipating the sonic advantages of a cleaner path. It just didn't sound as good as before and when I reverted to adding my ancient Rega Cursa 1 back in the chain the beautiful sound was restored. The difference in sound was very real (less 'life'?) and immediately noticeable - both ways. I really wasn't expecting that and chances are good you will see a positive difference too.

Whats the workaround? 

You can use any unused input on the stereo preamp for the preouts of the AVR.  The only thing you need to do is set a repeatable fixed volume level on the stereo preamp (say 9:00 or 12:00) and then set your multichannel speaker volume levels as usual.  When you wanna do HT you just choose that input on the stereo pre and turn its volume knob to the predetermined level and you’re good to go.  I did this for a year with no problem before I got a dedicated listening room. 

I’ve had good luck with class D amps and a tube preamp. I would think the schiit one would likely be an upgrade although I haven’t heard one. Just hearsay. 
 

For 500 ish bucks could try a used Jolida Fusion preamp if you can find one. I find Jolida stuff very underrated. Especially their tube DAC. I’m looking or another one. 

What Tektons did you buy? Don’t let the haters fool ya they are superb! I’m listening to my new Nebos now. Borderline epic! 

Get Return Privilege's for anything you try, compare, don't lose all the conveniences/features of something you have until you hear an improvement.